Find the Line Integral Of $\vec{F}=(3 x-2 y) \vec{i}+(3 x+5 y) \vec{j}$

question 25

Essay

Find the line integral of $\vec{F}=(3 x-2 y) \vec{i}+(3 x+5 y) \vec{j}$ around the curve consisting of the graph of y = xⁿ from the origin to the point (1, 1), followed by straight lines from (1, 1)to (0, 1)and from (0, 1)back to the origin.

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Definitions:

Psychosocial Task

A challenge proposed by Erik Erikson that individuals must navigate at each stage of life to develop psychologically in a healthy manner.

Autonomy Versus Shame

A stage in Erik Erikson's theory of psychosocial development in which children learn to exercise will and make choices, facing the challenge of autonomy versus shame and doubt.

Autonomous

Having the ability or freedom to act independently, make one's own decisions, and govern oneself.

Self-reliance

The reliance on one's own capabilities, judgment, or resources.